Development of a cohesive finite element method for fracture simulation
The phenomenon of crack propagation is among the predominant modes of failure in many natural and engineering applications, often leading to severe loss of structural integrity and catastrophic failure. Thus, ability to understand and simulate the evolution of crack propagation is very important issue in applied mechanics and structural engineering.
The work presented here focuses on the crack propagation using cohesive finite element methods, through the development and implementation of a FORTRAN code for the numerical simulation of the dynamic crack growth, which represent the cracks as displacement discontinuities across a surface of zero measure. This approach uses material constitutive law that relates stress and strain for the bulk solid constituents and a constitutive traction-separation law for cohesive surfaces. The material constitutive relation is characterized as an isotropic hyperelastic solid. The cohesive surface constitutive relation allows for the creation of new surfaces which serve as a path for the crack to propagate. The cohesive zone model used for the development of the code is based on the exponential type of traction-separation law formulated by Xu & Needleman. Numerical analyses carried out, concern failure in the forms of crack propagation and microcrack formation.
Dynamic crack growth is analyzed using numerical simulations for a plane strain block with initial central crack subject to tensile loading conditions. Analysis of the phenomenon of crack nucleation, growth and coalescence from pre existing defects in the plane block is conducted. A convergence test is conducted to study the effects of mesh size in the cohesive zone method. Finally, the simulation of wave propagation due to high speed impact is conducted.
The numerical simulation results have shown that the method has successfully captured the phenomenon of initiation, growth and coalescence of the crack, leading to the failure of the material system. The results for crack propagation show that, with the increase in the velocity boundary condition, there is less crack growth before branching. The results also show that the damage evolution and the crack growth are strongly dependent on the loading conditions. From the results for materials with defects, it is observed that as there is high number of defects there is more crack branching, i.e. more the defects, weaker is the material and easier to develop the cracks. The numerical simulation results for the convergence test suggested that the method provides convergent results for different mesh sizes.